Test the Given Claim About the Means of Two Populations

question 12

Essay

Test the given claim about the means of two populations. Assume that two dependent samples
have been randomly selected from normally distributed populations. A coach uses a new
technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores
were recorded before and after the training. The results are shown below. $$\begin{array} { l | c c c c c c c } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline \text { Before } & 9.5 & 9.4 & 9.6 & 9.5 & 9.5 & 9.6 & 9.7 \\\hline \text { After } & 9.6 & 9.6 & 9.6 & 9.4 & 9.6 & 9.9 & 9.5\end{array}$$ Using a 0.01 level of significance, test the claim that the training technique is effective in raising
the gymnasts' scores. Include your null and alternative hypotheses, the test statistic, P-value or
critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your
answer.

---

Definitions:

Excess Cash

The amount of cash owned by a business that exceeds its immediate operational and investment needs, often signaling financial strength.

Equity Financed

Refers to the method of funding a company or its operations through selling shares of stock to investors, rather than acquiring debt.

Market Price

The current value at which an asset or service can be bought or sold in a marketplace.

Ex-dividend

The ex-dividend date is the date on which a stock begins trading without the entitlement to receive the most recently declared dividend, meaning buyers from that day onward will not receive the dividend.